Halide perovskites as disposable epitaxial templates for the phase-selective synthesis of lead sulfochloride nanocrystals

Colloidal chemistry grants access to a wealth of materials through simple and mild reactions. However, even few elements can combine in a variety of stoichiometries and structures, potentially resulting in impurities or even wrong products. Similar issues have been long addressed in organic chemistry by using reaction-directing groups, that are added to a substrate to promote a specific product and are later removed. Inspired by such approach, we demonstrate the use of CsPbCl3 perovskite nanocrystals to drive the phase-selective synthesis of two yet unexplored lead sulfochlorides: Pb3S2Cl2 and Pb4S3Cl2. When homogeneously nucleated in solution, lead sulfochlorides form Pb3S2Cl2 nanocrystals. Conversely, the presence of CsPbCl3 triggers the formation of Pb4S3Cl2/CsPbCl3 epitaxial heterostructures. The phase selectivity is guaranteed by the continuity of the cationic subnetwork across the interface, a condition not met in a hypothetical Pb3S2Cl2/CsPbCl3 heterostructure. The perovskite domain is then etched, delivering phase-pure Pb4S3Cl2 nanocrystals that could not be synthesized directly.

Accretion of larger Pb3S2Cl2 NCs. Larger Pb3S2Cl2 NCs were obtained through a seeded growth approach, consisting in reacting crude Pb3S2Cl2 NCs obtained by direct synthesis with a stock solution of PbCl2 and Pb(SCN)2 at 170°C. During the dropwise addition of the stock solution, the heat decomposed Pb(SCN)2. This acted as a source of free sulfur that, reacting with the PbCl2 dissolved in solution, contributed to the accretion of Pb3S2Cl2 NCs. The progress of the reaction was tracked by taking aliquots of the reaction mixture at T = 0h, 1h, 2h, 4h, and 5h:15min (reaction halted), which were analyzed by TEM (Supplementary Figure 2). Preliminary tests performed by using equimolar amounts of PbCl2 and Pb(SCN)2 resulted in the formation of large amounts of an impurity tentatively identified as platelets of (OLA)2PbCl4 (Supplementary Figure  3a, orange plot), which could not be removed and made the reaction product unsuitable for further studies. Increasing the relative amount of Pb(SCN)2, that corresponds to the reaction conditions described in the Methods section of the Main Text, prevented the formation of such impurity and resulted instead in the nucleation of PbS impurities starting from ∼4h into the process. Those however grew significantly larger than the Pb3S2Cl2 NCs NCs size distribution (inset) was estimated using the software FIJI-ImageJ 1 by adapting the method described in Ref. 2 on a total of 250 NCs. After the accretion, the size distribution in the sample appears to be bimodal (two blue gaussians in the inset), but it is still roughly captured by a single gaussian distribution (red in the inset). Source data are provided as a Source Data file.

Structural characterization of Pb3S2Cl2 nanocrystals
Supplementary Figure 5: Attempt to fit the Pb3S2Cl2 NCs pattern based on the Pb3Se2Br2 cubic prototype. The XRPD experimental data (blue) and fit profile (orange) are plotted in the Cu-Kα 2θ scale to ease the comparison with patterns collected with lab-grade instruments. In correspondance of the peaks (e.g. 2θ = 31.3° and 37.0°), the residual curve (grey) clearly indicates that the simulated peak position is off with respect to the experimental one. However, the simulated peak at 31.3° falls at lower angles if compared with the measurement (i.e., longer periodicities), while the peak at 37.0° falls at higher angles (i.e., shorter periodicities). This kind of mismatch cannot be complensated by simply resizing a cubic unit cell, and requires to take into consideration a lower symmetry structure. Source data are provided as a Source Data file.
Single-Nanocrystal 3D-ED experiments and ab-initio structure solution of Pb3S2Cl2. 3D Electron Diffraction (3D-ED) 3,4 was exploited to solve the structure of Pb3S2Cl2 NCs. 3D-ED data were collected from roughly spherical NCs with a diameter of ∼25 nm, prepared as described in the Supplementary Discussion, section 1. During the data acquisition the electron beam was stationary, while the sample was tilted in fixed steps of 1° for a maximum total range up to 110°. In fact, diffraction data acquired with a precessing beam 5,6 were blurred due to the small size of the particles, and thus were not suitable for the 3D reconstruction. Therefore, only the data acquired with a stationary beam were used, with a consequent deterioration of the accuracy on the integrated intensities of reflections. The data were first analyzed using ADT3D 7 for the cell and space group determination, which resulted in a primitive triclinic unit cell with parameters The panels relative to the monoclinic lattice (b-d) are indexed accordingly to the unit cell choice proposed by the indexation software, prior to the standardization of the unit cell that we later performed on the refined Pb3S2Cl2 structure model.
Due to the small size of the NCs, the resolution of the collected datasets was limited to about 1.0-1.5 Å. Nevertheless, we attempted an ab-initio structure solution. The intensity integration for the structure determination was performed with in-house MATLAB routines, while the solution was performed using direct methods implemented in the software SIR2014. 8 The data were treated within the kinematical approximation: Ihkl ∝ F 2 hkl. The first solution attempt was performed in space group I-43d, the same reported for Pb3Se2Br2, 9 and produced a model with comparable atom distribution and connectivity. This evidence strengthened the hypothesis that Pb3S2Cl2 was indeed derived from such prototypal structure. An analogue solution was obtained in the space group I213 (Supplementary Figure 7a), a subgroup of I-43d that allows to assign different crystallographic positions to sulfur and chlorine (while in the I-43d they randomly occupy the same position). A second attempt, performed in the Cc space group, produced a similar, yet distorted structure (Supplementary Figure 7b). In all the cases, the Pb atoms could be unambiguously identified, while Cl and S could not be distinguished because of the very similar scattering factors. Figure 7: Pb3S2Cl2 structure solutions obtained from 3D-ED data. The two solutions were obtained a) in the space group I213 and b) in the space group Cc. The sulfur and chlorine species are tentatively assigned, due to the insufficient difference in the scattering factors. The unit cell choice is shown prior to the standardization that we performed later on the refined Pb3S2Cl2 model (black lines). Atoms color code: Pb = grey; S = yellow; Cl = green.

Supplementary
Ab initio structure solution of Pb3S2Cl2 from X-Ray Powder Diffraction (XRPD). The main sources of uncertainty in the 3D-ED solution were the low resolution of the dataset and the potential inaccuracies of the integrated intensities of reflections, due both to the secondary scattering phenomena, which were neglected by treating data within the kinematical approximation, and mostly to the inability to acquire data in precession mode. For this reason, we relied on XRPD data collected at the 28ID-2 beamline of the National Synchrotron Light Source (NSLS-II) of the Brookhaven National Laboratory to reattempt an ab-initio solution and then refine the structure of Pb3S2Cl2 NCs.
The ab initio structure solution by XRPD data was carried out using EXPO2014, 10 a software package that implements all the steps of the process: indexing, space group determination, full pattern decomposition, structure solution, structure optimization, and Rietveld refinement. The first two steps (i.e., indexing and space group determination) were highly challenging for our specific sample, as the expectedly minor distortions from the prototypal Pb3Se2Br2 cubic structure 9 and the severe size-related broadening of the diffraction features produced an extreme overlap of the reflections. This in turn caused the failure of the indexing routine, and introduced unavoidable errors in the intensity integration, that led the automatic space group determination process to produce incorrect results. Hence, the indexation and space group determination steps were performed by drawing from the information provided by 3D-ED. The following monoclinic cell parameters, initially determined by 3D-ED data and further optimized by Pair Distribution Function (PDF) analysis, were supplied as input values to EXPO2014: The space group Cc, suggested by 3D-ED, was used to estimate the integrated intensity of reflections and consequently also the structure factor moduli required for solving the crystal structure by Direct Methods. Among the possible cells identified by 3D-ED, the Cc monoclinic choice was preferred based on the best agreement between the calculated and the experimental positions of reflections. The application of Direct Methods produced twenty sets of phases, ranked according to a combined figure of merit. An automatic procedure was applied to select the best candidate from each set based on the agreement factor between the observed and calculated structure factor moduli. Remarkably, the first ten models by rank were in great overlap with each other and with the structure determined by 3D-ED, the major differences being due to the ambiguous assignment of the sulfur and chlorine positions. Out of these 10 solutions, one was selected via the graphic user interface of EXPO2014 according to structural chemistry considerations (e.g., adjacency of cations and anions, homogeneity of the coordination environment for atoms of the same element, etc.). This selected model then underwent a first optimization through the Rietveld refinement routine implemented in the EXPO2014 package.
Combined XRPD + PDF refinement of the Pb3S2Cl2 NCs structure. The structure model obtained from the ab-initio XRPD solution was refined by combining the analysis of XRPD and PDF data, both collected at the 28ID-2 beamline at NSLS-II. It is important to note that the two datasets, XRPD and PDF, are independent from each other as the position of the detector was changed for the two experiments.
The PDF profile was refined by using the programs PDFGUI [11][12][13] and DiffPy-CMI 16 . The fit was performed for interatomic distances (r) above 1.5 Å, to avoid finite-size artifacts in the low r range, and up to 50 Å, with a step of 0.05 Å. At first, Python scripts were used to perform an automatic refinement where all the parameters were optimized one at a time, while keeping constant all the others. The parameters were refined in the following order: scale factor, lattice parameters, Qbroad, (peak broadening from increased noise intensity at high Q), δ1 (coefficient for the 1/r contribution to the peak sharpening), atomic displacement parameters, and atomic coordinates. During the refinement, the crystal symmetry was exploited to constrain lattice, displacement parameters, and atomic coordinates. The refinement ran for a total of 20 cycles: during the first 10, the atomic displacement parameters were kept isotropic, while they were set to anisotropic in the last 10 cycles.
As a second step, the structure was refined interactively starting from the model resulting from the first step. At this stage, the fitting parameters were refined to treat structural distortions and outlier parameters. The structure optimization was carried out by alternating refinement procedures in the direct space (PDF) and in the reciprocal space (XRPD, through the EXPO2014 refinement routine). We choose to alternate PDF and XRPD refinements to avoid overfitting and local minima, exploiting the fact that the PDF and XRPD profiles we collected were not related by a simple Fourier transform, since the position of the detector was different for the two experiments. This allowed optimizing the experimental setup for both measurements, hence allowing us to make the best use of complementary information in both the direct and reciprocal spaces to drive the structure refinement.
Supplementary Figure 8 shows the asymmetric unit of the refined structure and its local environment. The observed, calculated and difference profiles resulting from the last cycle of the Rietveld and PDF refinements are shown in Figure 2d  β (°)

144.547(8)
Supplementary Table 3: Results of the PDF refinement of Pb3S2Cl2 NCs. Goodness of fit and unit cell parameters obtained during the last cycle of the PDF fit for Pb3S2Cl2 NCs. Rw is the weighted agreement factor between observed and calculated PDF, δ1 is the coefficient for 1/r contribution to the peak sharpening, Qbroad describes the peak broadening from increased intensity noise at high Q, SPdiameter is the particle diameter for PDF shape damping function.

PDF refinement of Pb3S2Cl2
Rw 0.155 , where di are the distances between couples of corresponding i th atoms in the two compared models, and Nau is the total number of atoms in the asymmetric unit).
Supplementary Figure 9: Pb3S2Cl2 structure models from 3D-ED and XRPD+PDF compared. The Pb3S2Cl2 structure models obtained by 3D-ED (black) and by XRPD+PDF (red) demonstrate a strong overlap. In this image, the elements are differentiated by size (Pb = large atoms; S/Cl = small atoms). Both structures are shown after applying the crystal data standardization routine implemented in VESTA. 14 Crystal data standardization. As a final step after the refinement, we applied the crystal data standardization routine implemented in the software VESTA 14 to produce the Pb3S2Cl2 structure model that is shown in Figure 2e Figure 5f of the Main Text, reveals that these states concentrate at the chalcohalide surface, similar to what we observed for Pb4S3Br2/CsPbCl3 heterostructures in the past. 15 In this case however, the first delocalized states at both the CB and the VB edges also appear to be dominated by the Pb4S3Cl2 system ( Figure 5e of the Main Text), suggesting a type-I energy level alignment.
Supplementary Figure 12: Pb4S3Br2/CsPbCl3 heterostructure atomistic model. The atomistic Pb4S3Br2/CsPbCl3 heterostructure model built to perform DFT calculations is here shown before (left) and after (right) the structure optimization. The two models appear very similar because both the Pb4S3Br2 and the CsPbCl3 moieties were pre-optimized before assembling the heterostructure model. Atoms color code: Cs = cyan; Pb = grey; S = yellow; Cl = green.

Structure refinement of Pb4S3X2 nanocrystals and comparison with Pb3S2Cl2
Combined XRPD+PDF structure refinement of Pb4S3Br2 and Pb4S3I2 NCs. We refined the structure of Pb4S3Br2 and Pb4S3I2 NCs, that we already reported in our prior publication, 16 in order to better compare such phases with the Pb3S2Cl2 structure that was solved in this work. In addition, we want to provide the community with more reliable structure models than those we reported by us in the past, as they were refined only on lab-grade XRPD data. Hence, at NSLS-II we collected XRPD and PDF data on Pb4S3Br2 and Pb4S3I2 NCs, and we refined both structures following a procedure analogue to that detailed in the Supplementary Discussion, section 2. The outcome of the analyses is summarized in the Supplementary Figures 13-14 Table 4: XRPD and PDF refinement parameters for Pb4S3Br2 and Pb4S3I2 NCs. For XRPD, Rp is the agreement factor between observed and calculated profile, Rwp is the weightedprofile reliability parameter, χ 2 is the chi-squared value, GoF is the Goodness of Fit. For PDF, Rw is the weighted agreement factor between observed and calculated PDF, δ1 is the coefficient for 1/r contribution to the peak sharpening, Qbroad describes the peak broadening from increased intensity noise at high Q, SPdiameter is the particle diameter for PDF shape damping function. It is worth noting that the quality of the XRPD Rietveld fit for Pb4S3Br2 is not optimal, and there are some discrepancies in the unit cell parameters as refined by XRPD and PDF. We attribute this to a combination of an intrinsically challenging fit for XRPD, where many relevant reflections overlap due to their small relative angular distance and to the intrinsic size-related broadening of diffraction features, plus some possible small deviations from the ideal orthorhombic symmetry in which the structure was refined. Those might reflect on the slight deviations between observed and calculated PDF profiles at large interatomic distances (r > 40 Å), and affect the overall quality of the XRPD fit. However, given the minor relevance of the Pb4S3Br2 refinement in this work, we decided not to investigate further. Figure 15 compares the refined structures of the three compounds we examined, with a focus on the coordination polyhedra of each element. As discussed in the Main Text, the Pb and S atoms share similar coordination environments in all the three compounds. Conversely, Cl has a different coordination in Pb3S2Cl2 (6 Pb atoms, distorted octahedral) than Br and I in Pb4S3X2 (7 Pb atoms, pentagonal bipyramid), pointing to the influence of the halide ionic radius in determining which stoichiometry and structure is favored during the formation of free-standing lead sulfohalide NCs. Figure 15: Refined Pb3S2Cl2, Pb4S3Br2, and Pb4S3I2 structures. The three structures are represented highlighting the coordination polyhedra of each non-equivalent crystallographic position. The column on the right compares the coordination polyhedra of lead (top), sulfur (middle) and halides (bottom) in the three compounds. The structures shown here for Pb4S3Br2 and Pb4S3I2 come from the last refinement cycle of the PDF analysis, that has the advantage of prioritizing the accuracy of the local coordination environment if compared to the Rietveld XRPD analysis. Atoms color code: Pb = grey; S = yellow; Cl = green; Br = brown; I = purple.

Supplementary
Comparison of Pb3S2Cl2, Pb4S3Br2, and Pb4S3I2 PDF profiles. Further insights on the role of the halide radii in Pb3S2Cl2, Pb4S3Br2 and Pb4S3I2 come from interpreting their PDF profiles (Supplementary Figure 16) with the help of the structure models produced from the refinement. Indeed, the peaks corresponding to Pb-S distances correspond approximately to the same interatomic distance in all compounds (solid black arrow, Pb-S ∼2.85 Å). Conversely, the Pb-X bonds (dashed arrow) expand from 2.9 Å in Pb3S2Cl2 to 3.3 Å in Pb4S3I2, consistently with the increasing ionic radii. Interestingly, the Pb-Pb distances (dotted arrow) follow an opposite trend, as they decrease from ∼4.1 Å in Pb3S2Cl2 to ∼3.8 Å in Pb4S3I2. Together, these two facts highlight how the expansion of the coordination environment around the halide atoms, captured by the elongation of the Pb-X bond lengths, forces the material to adopt a more compact structure for Br and I with respect to Cl. This is also captured by the calculated density, which raises from 6.95 g/cm 3 for Pb3S2Cl2 to ∼7.38 g/cm 3 for both Pb4S3Br2 and Pb4S3I2. Figure 16: PDF profiles of Pb3S2Cl2, Pb4S3Br2 and Pb4S3I2 NCs compared. The evolution of the Pb-S, Pb-X and Pb-Pb distances is indicated by solid, dashed and dotted arrows, respectively. The profiles have been normalized, and were offset vertically by an arbitrary constant for representation purposes. The program RootProf 19 was used to elaborate and visualize the PDF profiles. Color code: Pb4S3I2 = red, Pb4S3Br2 = purple, Pb4S3Cl2 = blue. Source data are provided as a Source Data file.

Models of Pb4S3Cl2/CsPbCl3 heterostructures
Cationic subnetwork in Pb4S3Cl2/CsPbCl3 heterostructures. The role of the cationic subnetwork in the formation of the Pb4S3Cl2/CsPbCl3 heterostructures, and its similarity with the Cs-Pb-X/CsPbX3 epitaxial heterojunctions, can be better visualized by comparing its structure with those of CsPb2Cl5/CsPbCl3 (left) and Cs2PbCl4/CsPbCl3 heterostructures (Supplementary Figure 17). In all the three models the perovskite CsPbCl3 moiety remains unchanged.
The first comparison highlights that both Pb4S3Cl2 and CsPb2Cl5 share planar polyanions with identical geometry laying parallel to the epitaxial interface plane. The same polyanion is shown as seen from above in Figure 3a of the Main Text. In both structures the polyanions are enclosed in a subnetwork of cations, here shown in orange, that is composed of Cs + in the case of CsPb2Cl5 and of Pb 2+ in the case of Pb4S3Cl2. The fact that such subnetwork matches exactly that of CsPbCl3 has a key role in allowing the growth of the heterostructure.
The second comparison highlights the similarities between the cationic subnetworks of Pb4S3Cl2 and Cs2PbCl4. The different positioning and nature of polyanions causes it to be more compressed in Pb4S3Cl2 with respect to Cs2PbCl4, but the general distribution of cations, forming cuboidal cages shifted with respect to each other by half lattice step (resulting in the formation of triangular motifs along the projection shown), is identical in both structures. We must note here that we are comparing Pb4S3Cl2/CsPbCl3 with two hypothetical heterostructures because: I. The CsPb2Cl5/CsPbCl3 interface has never been reported, although there are reports of analogue CsPb2Br5/CsPbBr3 heterostructures. 17,18 II. The Cs2PbCl4 structure does not exist, and the closest comparison would be with a CsPbI2Cl2/CsPbCl3 heterostructure, as CsPbI2Cl2 is the only known member of the Cs2PbX4 family of compounds. However, although this heterostructure has never been reported, the Cs + subnetwork preservation principle we outlined in our previous work on Cs-Pb-X compounds 19 allows to predict with good confidence how it would look like.  The three Pb4S3X2 NCs patterns feature strong similarities in terms of general distribution and intensity of diffraction peaks, further confirming the that the NCs obtained by etching the heterostructures retain the Pb4S3Cl2 structure. However, a more elaborate analysis of the diffractogram is hindered by the extreme peak broadening and the overall low quality. To improve the data visualization, a moving-average smoothing algorithm was applied to some of the patterns (Pb4S3Cl2, CsPbCl3, heterostructures). Color code: Pb4S3Cl2 = blue, Pb4S3I2 = red, Pb4S3Br2 = purple, Pb4S3Cl2 = orange, Pb4S3Cl2/CsPbCl3 heterostructures = black, CsPbCl3 = cyan. Source data are provided as a Source Data file.